Physics Beyond the
Standard Model
Summary by Dennis Silverman
Physics and Astronomy
UC Irvine
Where Does Mass Come From?
The electroweak “gauge” theory only has
conserved currents for its weak charges if the
W’s and Z are massless, like the photon is. It
also helps if quarks and leptons are massless in
the Energy.
 To maintain this, but yet have physical masses,
we fill the vacuum with some sludge. A particle’s
mass is then proportional to the amount each
particle couples to this sludge.
 The sludge is the everywhere constant vacuum
value of the neutral Higgs.

The Higgs Fields in the SM



Three extra Higgs fields,
H+, H-, anti-H0 make up
the extra component of
the W and Z spins
needed to make them
massive.
The W’s have a mass of
81 GeV, and the Z of 90
GeV.
The H0 has a constant
vacuum density, and can
also make a physical
particle.
H  H 0 

, 

H0  H 

 

How to Find the Higgs

The Higgs vacuum value is uniform, neutral, appears the
same at all velocities, and undetectable – except for the
fact that it gives mass to everything.
 A particle’s mass is proportional to its coupling to the
Higgs and therefore to its vacuum density.
 The excitations of the Higgs is a real particle, predicted
to be at about 115-130 GeV.
 This should show up in the LHC in some rare decays.
 It would have shown up at the Fermilab Tevatron, except
that the intensity has not met expectations.
Increasingly General Theories
 Grand
Unified Theories of electroweak
and strong interactions
 Supersymmetry
 Superstring Theories – 10 dimensions with
gravity
 Superstring Unification to M Theory
Running Coupling Constants

Charged particles have virtual quantum allowed clouds
around them of photons and electron-positron pairs.
 Colored particles have virtual gluons and q-anti-q pairs.
 So the total coupling at long distance or “charge”, is
different from the coupling at short distance, where the
the cloud is penetrated.
 Electromagnetic coupling 1 = e2/c increases with
energy from 1/137 to 1/40 at 1017 GeV Unification Scale
 Strong coupling 3 = g2/c decreases from ~1 to 1/40
 Weak coupling to W’s is 2.
 So couplings come together at unification scale
g3
g3
Running Gluonic Coupling
3 = (g3)2 /c
Running Couplings
Fundamental Particles for Unification

Unification means that at a GUT scale, where masses
can be ignored, all fundamental particles appear in the
same multiplet.
 This allows their charges to be the same or given
fractions of each other, and accounts for the proton and
electron charge being equal.
 The particles from the SM to include for the first
generation are the 16 (left handed):
ur ug ub dr dg db anti-(ur ug ub dr dg db)
e e- anti-e e+
 Recently, neutrino oscillations and mass were found,
adding the anti-e.
 In the GUT, there are vector bosons that take
fundamental particles into another in the multiplet.
Sequence of GUTS

Standard Model of electroweak doublets for quarks and
leptons plus photon (SU(2)xU(1)) and three colors
(xSU(3)). It has , W±, Z, and 8 gluons as bosons.
 Combine 3 colors and electroweak doublet (SU(5)) –
ruled out as causes proton decay at level not seen – has
5 + 10 fundamental particles. It has 24 bosons.
 Add extra neutrino mode for massive neutrinos – 16
fundamental (SO(10))
 There are 45 gauge bosons in SO(10).
 27 fundamentals (E6), including singlet quarks and
neutrinos.
 E7, E8 (heterotic string)
 Three generations of each fundamental multiplet
A Bit of History of Unification

Electricity unified with magnetism (M. Faraday and J. C.
Maxwell).
 Relativity and General Relativity (A. Einstein).
 Quantum Mechanics (Planck, Bohr, Schrodinger and
Heisenberg).
 Relativistic quantum mechanics (P. Dirac).
 Quantum Electrodynamics (R. Feynman, Tomonaga,
Schwinger).
 Quarks and Quantum Chromodynamics (Nemann, M.
Gell-Mann and G. Zweig).
 Unification of Electromagnetism with Weak Interactions
to form Electroweak theory (S. Weinberg, A. Salam).
 Grand Unified Theories
 Supersymmetry
 Superstring Theory of Everything including gravity.
Proton Decay

In a GUT there are X and Y gauge bosons that
can transform a quark into an antiquark, and a
quark into a lepton, since they are in the same
multiplet.
 This allow protons in quarks to decay into a
lighter pi or K meson and a lepton.
 Don’t worry, the lower limit on the lifetime is 1034
years, far longer than the age of the universe of
1010 years.
 It takes a detector the size of Super-K to see a
few proton decays a year in these theories.
Proton Decay
dr
dr
ug
anti-danti-r
P
ub
Xanti-r
e+
p0
Particle Spin

Orbital angular momentum is quantized to
integer units of Planck’s constant over 2p:
 = h/2.
 Quarks and leptons have half a unit of
angular momentum as spin, or are spin 1/2
particles, also called fermions.
 Photons and W’s and Z are spin 1 particles,
also called bosons.
 Gravitons have spin 2, and are bosons.
Particle Supersymmetry





In a Grand Unified Theory, all quarks and leptons are in
a generation are united into one family.
The GUT gauge bosons transform one quark or lepton to
another, such a gluon changing one color quark into
another.
A grander symmetry would be to transform all gauge
bosons to fermions with the same charges, and vice
versa.
Thus for every spin ½ fermion there would be a spin 0
boson with the same charges and flavor, and to every
gauge boson, there would be a like charged and coupled
spin ½ fermion.
These look-alikes, except for spin, are called sparticles.
Conserved Supersymmetry

If supersymmetryness is conserved, sparticles can only
be created or destroyed in pairs
 Sparticles would then decay to the ordinary particles plus
another sparticle,
 until they reach the lightest supersymmetric particle
(LSP)
 The LSP should be neutral and is a leading dark matter
candidate
 They should have masses about 1 TeV
 They should be produced in pairs at the LHC in 2007
 The Next Linear Collider (NLC) will be needed to map
out the sparticles and Higgs interactions in detail.
Sparticle Names






Thus with quarks there would be spin 0 squarks
Leptons would have spin 0 sleptons (selectron
and sneutrino)
The photon also would have a spin ½ photino
The W’s and Z’s would have spin ½ Winos and
Zinos (after Wess and Zumino)
Spin 0 Higgs would have spin ½ Higgsinos
In a supergravity theory, spin 2 gravitons have
spin 3/2 gravitino look-alikes.
Why Supersymmetry (SUSY)?
It’s believers think it is a beautiful symmetry between
fermions and bosons, and should be a part of nature.
 If the sparticles are at about 1 TeV, then the running
coupling constants actually do meet at a GUT scale of
1017 GeV.
 GUT scale (mass) Higgs’s would normally couple to the
light SM Higgs and bring its mass up to the GUT scale.
 Adding sparticles to particles cancel this coupling to
leave the SM Higgs light, solving the so-called Heirarchy
problem.
 String Theory requires SUSY, again for similar
cancellations.

Minimal SUSY Standard Model






The MSSM has two Higgs doublets, as opposed
to the one in the standard model.
The doublets also have distinct anti-Higgs.
Thus there are 8 Higgs particles.
Three are “eaten” to make the W± and Z
massive.
One makes the neutral mass generating Higgs.
Four more are observable, of which two are
charged.
Evolution of Gauge Couplings (reciprocals)
Standard Model
Supersymmetry
Meeting of the Running Couplings
(reciprocals) in MSSM
What is String Theory?

It is the theory that elementary particles are really strings
with tension, that obey relativity and quantum
mechanics.
 By dispersing the particle away from a point, it avoids
infinities in the treatment of gravity or gravitons by
pointlike particles.
 The string size is close to the Planck size of 10-32 cm,
which is the smallest size where gravity becomes strong.
 To avoid “anomaly” infinities requires supersymmetry
and 10 dimensions (1 time and 9 space dimensions).
 String theory then provides a quantum theory of gravity.
 Andre Neveu, John Schwarz, Michael Green and Pierre
Ramond were founders.
Pictures of John Schwarz and Ed
Witten
Types of Superstring Theories


There are five superstring theories.
There is one open superstring theory with left (L)
moving waves (SO(32)).
 There are two closed superstring theories:



Type IIA: L-R parity symmetric
Type IIB: L only, parity violating
There are two heterotic string theories of a
product of a string theory in 26 dim (with L
moving waves) x a superstring in 10 dim (with R
moving waves).

(SO(32)) and (E8 x E8).
Unification of Superstring Theories

Recently, in the second string revolution, it was
discovered that there are transformations
between all five superstring theories. (Ed Witten)
 This means they are all views of a larger theory
which is not well understood, but is called M
theory. It may be in 11 dimensions.
 For further information, see
http://superstringtheory.com/, run by Patricia
Schwarz, John Schwarz’s wife.
 “The Elegant Universe” by Brian Greene,
http://www.pbs.org/wgbh/nova/elegant
Towards Verification of
Superstring Theory

Since superstring theory included the three
unified forces of GUTS and gravity, it has been
called the Theory of Everything.
 It has not been possible to “solve” superstring
theory to find a unique physical model.
 There are a half-million ways to topologically
“compactify” the extra six dimensions to very
short distances, and leave the four dimensional
world that we live in.
 So many GUTS and breakup paths of GUTS to
the SM are still possible
Verification of Superstring Theory



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The masses of sparticles are not well predicted.
If they are in the TeV range, they will appear in the LHC.
Once they are found, the NLC e+ e- collider will more
precisely determine their properties.
The convergence of the running coupling strengths at a
GUT scale is more successful with SUSY particles than
in the SM.
If SUSY is found, it will be considered a success of string
theory. If not found, it could spell its demise.
The lightest neutral SUSY particle (LSP) could be dark
matter, and there are experiments to directly detect
them, but they will take a while to reach large enough
scale.
How do strings scatter?
 Via
the “pants” diagram, where two strings
merge to one, and then go back to two.
Speculative Models of Extra
Dimensions
 Large
Extra Dimensions and Branes
 Early Unification with a Strong Gravity
Brane Solutions





String Theories have membrane solutions
The most used is that all our 4 dimensional
world is a membrane in the 10 dimensional
world.
Open string ends are attached to the membrane.
Quarks, leptons and interacting bosons for
strong and electroweak particles are confined to
the brane.
But gravitons as closed strings can leave the
brane and spread out in the extra dimensions.
Brane with attached string
and graviton in extra dimension
Large Extra Dimension Models




By experimental limits, extra dimensions could still be as
large as 0.1 millimeter, and this will be tested by gravity,
which behaves as F ~ M1 M2/ rn+2 for n extra
dimensions, at r < R.
In these, gravity could become strong at 1 TeV and unify
with the other forces there. (Nima Arkani-Hamed,
Dimopoulos and Dvali)
The extra dimension could be curled up with 1 TeV
excitations, or at the String or Planck Scale.
The former would show up in experiment at Fermilab or
the LHC as invisible missing energy disappearing into
the extra dimensions in excitations there, or as one
micro black hole a second being produced.
Plane Extra Dimension

The extra dimension could be between two flat branes,
one of which is physical, and one of which has gravity
(unphysical brane).
 The gravity field exponentially decreases from the
unphysical to the physical brane.
 Thus gravity appears weak to us on the physical brane,
but is strong on the unphysical brane.
 Called the Randall-Sundrum model.
 The extra dimension models so far do not give GUT
theories, spoiling the supersymmetry triumph of
explaining the convergence of coupling constants at the
GUT scale.
Relevance of Particle Physics

We are closer to accounting for some leftover matter,
possibly requiring three generations of quarks and
leptons.
 We may someday account for inflation and dark matter
(SUSY?) and dark energy.
 We understand how the Sun shines through weak
interactions.
 We understand how color forces and quarks form
nucleons.
 We may soon find how a Higgs gives mass to
everything”.
 There may be Grand Unification to keep charges of
everything the same and allow particle changing
interactions.
 We may have found a way to have gravity that is
consistent with quantum mechanics.